Hydrocarbon Sorption in Flexible MOFs—Part I: Thermodynamic Analysis with the Dubinin-Based Universal Adsorption Theory (D-UAT)

Abstract

The analysis of empirical sorption equilibrium datasets is still vital to gain insights into material–property relationships as computational methods remain in development, especially for complex materials such as flexible MOFs. Therefore, the Dubinin-based universal adsorption theory (D‑UAT) was revisited and evaluated as a simple visualization, analysis, and prediction tool for sorption equilibrium data. Within the theory, gas properties are normalized into corresponding states using the critical temperatures of the respective sorptives. The study shows theoretically and experimentally that the D-UAT is able to condense differences of sorption data visualized in reduced Dubinin plots to just three governing parameters: (a) the accessible pore volume, (b) the reduced enthalpy of sorption, and (c) the framework’s reduced free energy differences (in case of flexible behavior). This makes the theory a fast visualization and analysis tool, the use as a prediction tool depends on rough assumptions, and thus is not recommended.

Hydrocarbon Sorption in Flexible MOFs—Part II: Understanding Adsorption Kinetics

“…With this modeling, the boundaries of the structural transition or so-called gate-opening, herein referred to as gate-opening start ( GOS ) and gate-opening end ( GOE ), respectively, can be mathematically approximated using the excess surface work theory [ 42 ] (see Supplementary Information, Section S2 ). The precise thermodynamics governing the sorption process of the studied system, as well as the analytical framework utilizing the Dubinin theory, were investigated in a previous work [ 35 ]. The basic model conception of adsorption is summarized in the following.…”

“…Generally, the uptake in the low-pressure region up until the GOS is small, evidenced by a loading of 0.05–0.16 mole gas per mole unit cell (mol mol −1 ) for temperatures between 283 and 328 K. This can be interpreted as the adsorption of n -butane on the outer surface area and within the spatial of the pore entries on the np -form of the framework. However, as soon as a specific pressure is reached, the mp -form becomes energetically preferred [ 35 ]. Triggered by the adsorption stress that is exerted by the adsorptives within the pore entries [ 5 ], the structure is destabilized, pressed open, and thus, will start to switch into the larger pore form of the MOF—in a domain-by-domain mode [ 43 ]—and generate a microporous pore structure accessible for gas molecules.…”

“…Triggered by the adsorption stress that is exerted by the adsorptives within the pore entries [ 5 ], the structure is destabilized, pressed open, and thus, will start to switch into the larger pore form of the MOF—in a domain-by-domain mode [ 43 ]—and generate a microporous pore structure accessible for gas molecules. Due to different sizes of MOF particles and the analog distribution of energy needed to open the domains of the framework, as well as a kinetic hindrance that is assigned to the adsorption process specifically, the phase transition happens in a pressure range rather than at a sharp pressure point [ 35 ]. Once the structural transition is complete, further pressure increase leads to minor pore filling of the mp -form of 1 up to saturation loadings between 3.7 and 3.4 mol mol −1 in the investigated temperature range.…”

“…The MOF [Cu 2 (H-Me-trz-Ia) 2 ] ( 1 ) studied herein is part of an isostructural series of metal-organic frameworks built on Cu 2+ metal ions and triazolyl-isophthalate linkers [ 36 ]. The adsorbent was further presented in a recent publication regarding the thermodynamic analysis of the gate-opening using the Dubinin-based universal adsorption theory [ 35 ]. It was shown that the material switches from a narrow-pore form ( np -form) to a medium pore form ( mp -form) upon adsorption with n -butane while CO 2 can even trigger a second step towards a large-pore form ( lp -form).…”

“…Therefore, this work focuses on the investigation of the interplay between diffusion and the structural transition in a flexible MOF described by a mathematical model for gas uptake at various temperatures. Exemplary for a hydrocarbon/flexible MOF system, n -butane as a probe molecule on [Cu 2 (H-Me-trz-Ia) 2 ] ( 1 ) was studied, which was previously investigated thermodynamically [ 35 ]. Gravimetric uptake and IR diffusion measurements were conducted at different temperatures and for different pressure steps according to given adsorption isotherms.…”